A very bizarre weighted coin comes up heads with probability $\frac12$, tails with probability $\frac13$, and rests on its edge with probability $\frac16$.  If it comes up heads, I win 1 dollar.  If it comes up tails, I win 3 dollars.  But if it lands on its edge, I lose 5 dollars.  What is the expected winnings from flipping this coin?  Express your answer as a dollar value, rounded to the nearest cent.
Explanation: The expected value is $E = \left(\dfrac{1}{2}\times\$1\right) + \left(\dfrac{1}{3}\times\$3\right) + \left(\dfrac{1}{6}\times(-\$5)\right) = \$\dfrac{4}{6} =\boxed{\$\dfrac23 \approx \$0.67}$.